RATIONALE: Drugs used in chemotherapy, such as paclitaxel and docetaxel, work in different ways to stop the growth of tumor cells, either by killing the cells or by stopping them from dividing. Lapatinib may stop the growth of tumor cells by blocking some of the enzymes needed for cell growth. Monoclonal antibodies, such as trastuzumab, can block tumor growth in different ways. Some block the ability of tumor cells to grow and spread. Others find tumor cells and help kill them or carry tumor-killing substances to them. It is not yet known whether chemotherapy is more effective with lapatinib or trastuzumab in treating patients with breast cancer.

PURPOSE: This randomized phase III trial is studying chemotherapy and lapatinib to see how well they work compared with chemotherapy and trastuzumab in treating women with HER2/neu-positive metastatic breast cancer.

No history of other malignancies, except adequately treated ductal carcinoma in situ or lobular carcinoma in situ, adequately treated nonmelanoma skin cancer, curatively treated carcinoma in situ of the cervix, or other curatively treated solid tumor (non-breast) with no evidence of disease for ≥ 5 years

No serious cardiac illness or condition including, but not limited to, any of the following: